Herein, we choose approximate BD to design \( \lbrace {\mathbf {B}}_{g}\rbrace  \) . For this reason, we choose \( r_{g}^{\star }\le r_{g} \)  dominant eigenvalues of \({\mathbf {R}}_{g} \) . On this ground, we write \( {\mathbf {U}}_{g}=[ {\mathbf {U}}_{g}^{\star }, {\mathbf {U}}_{g}^{^{\prime }}] \) , where \( {\mathbf {U}}_{g}^{\star } \)  is the \( M \times r_{g}^{\star } \)  matrix consisted of the dominant eigenvectors and \( {\mathbf {U}}_{g}^{^{\prime }} \)  is the \(M \times (r_{g}-r_{g}^{\star }) \)  matrix including the eigenvectors corresponding to the weakest eigenvalues. To achieve approximate BD, we have to choose the dominant eigenmodes \( r_{g}^{\star } \)  for each group \( g \)  subject to the condition \(\mathrm {Span}({\mathbf {U}}_{g}^{\star }) \nsubseteq \mathrm {Span}(\lbrace {\mathbf {U}}_{i}^{\star }:i\ne g\rbrace )\)  for all groups \( g =1, \cdots , G\) . Notably, the design of \( \lbrace {\mathbf {B}}_{g}\rbrace  \)  has to take into account a feasible choice of the parameters \( \lbrace r_{g}^{\star }\rbrace  \) , \( \lbrace b_{g}\rbrace  \) , and \( \lbrace K_{g}\rbrace  \)  that should be optimized to maximize the SE under a given system setup. The matrix \( {\mathbf {B}}_{g} \)  is constructed as in [1]}. Herein, we briefly summarize the main steps. Hence, first, we define the matrix
\({\mathbf {U}}_{-g}=[{\mathbf {U}}_{1}^{\star },\ldots ,{\mathbf {U}}_{g-1}^{\star },{\mathbf {U}}_{g+1}^{\star }, \ldots , {\mathbf {U}}_{G}^{\star }],\) 
